Labour leader Jeremy Corbyn has met senior Jewish community chiefs for the first time since he was elected last year.
The Board said the session had "resulted in significant clarifications" of Mr Corbyn's views, but called on him to do more to address "profound and real concerns" about his past meetings with extremists and antisemites.
Mr Corbyn and two advisers held talks with Board of Deputies president Jonathan Arkush and chief executive Gillian Merron this afternoon.
Following the meeting Mr Arkush said: "We had a positive and constructive meeting and were pleased that Mr Corbyn gave a very solid commitment to the right of Israel to live within secure and recognised boundaries as part of a two state solution to the Israel-Palestine conflict.
"Mr Corbyn affirmed his support for shechitah, brit milah and Jewish faith schools. He also resolved in strong terms to fight antisemitism from wherever it comes.
"He rejected any sort of violence or intimidation such as occurred at King’s College London last month."
But Mr Arkush added: "Despite being pressed, he should do more to address profound and real concerns about past meetings with people or organisations with extremist or antisemitic views.
"We are also looking for the Labour leadership to show with more clarity that it will maintain its longstanding opposition of boycotts against Israel."
The meeting had been "the beginning of a conversation" between British Jews and the party, Mr Arkush said. A second meeting is planned for later this year.
Mr Corbyn said he was "looking forward to continuing that dialogue".
“I am a lifelong campaigner against racism and fascism in all forms, and I made it clear that I am utterly opposed to antisemitism in any form, including denial of the Holocaust, from any part of the political spectrum.
“The Jewish community is a vibrant and much valued part of our diverse UK society, and I will continue to defend the right to religious freedom and practice, including specifically shechitah and the brit milah, Jewish faith schools, and culturally sensitive youth and social care services.
“I have a long interest in campaigning for peace and justice in the Middle East, and reiterated my commitment to a two-state solution to the Israel-Palestine conflict. Israelis and Palestinians both have the right to a state, and to live in peace and security. I condemn violence - the future of the region can only be resolved with negotiation, not violence.
“The Israel-Palestine conflict is an emotive subject for communities in Britain too. But that can never be an excuse for antisemitism or Islamophobia.
"Disagreements over sensitive political issues, including the Middle East, must be conducted in a civil manner and without intimidation - I condemn all acts which intimidate or constrain the exercise of free speech."
Mr Corbyn said he was "determined to fight antisemitism and all forms of racism, and to work with representatives of the Jewish community in a constructive dialogue to improve interfaith relations and community safety".
Last summer’s Labour leadership election was dogged by media interest in Mr Corbyn's association with Holocaust deniers, antisemites and other extreme figures after the JC posed a series of questions for him to answer.
Mr Arkush had previously said the meeting would be "an acid test of how relations will be between the Labour Party and the Jewish community”.
In September, the Board leader pledged to seek an urgent meeting with Mr Corbyn if he won the Labour leadership election.
At the time Mr Arkush called on the Islington North MP publicly to reject Hamas and Hizbollah if he was to gain the trust of British Jews.
He said Mr Corbyn’s comments about the terrorist groups were one of the causes of the community’s concerns about the likelihood of him becoming leader.